Probability of ruin in discrete insurance risk model with dependent Pareto claims

Abstract

We present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails. The distributions in this class are zero-inflated discrete counterparts of the Pareto distribution. In particular, we obtain the probability of ruin in the compound binomial risk model where the claims are zero-inflated discrete Pareto distributed and correlated by mixture.

Keywords

• actuarial science
• compound binomial risk model
• dependence by mixture
• discrete pareto distribution
• geometric distribution
• heavy tail
• mixture
• power law
• ruin probability
• zero-altered distribution
• zero-inflated distribution
• zero-modified distribution